Nonequilibrium statistical mechanics of heterogeneous systems. I. Transport phenomena at an interface and the problem of boundary conditions

The approach is developed which enables us to study the transport processes in many-component heterophase systems, in particular, on the boundary between two volume phases. Conservation laws for densities of mass, energy and momentum are derived for volume phases and surface phase. In the quasiequilibrium approximation the conservation laws become closed and produce the ideal hydrodynamics system of equations. Transport laws for each phase are derived. For calculating average fluxes of the mass, energy and momentum in each of the three phases, the nonequilibrium distribution function is used which differs from the quasiequilibrium distribution function by the terms proportional to the gradients of the hydrodynamical parameters (temperatures, velocities and chemical potentials) of the three phases and their discontinuities on the boundaries between the surface phase and the volume ones. Inserting the transport laws into the conservation laws gives the nonideal hydrodynamics system of equations. In the particular case when the surface phase does not possess the surface mass and energy densities, the hydrodynamical equations of the surface phase degenerate into the system of relationships connecting the boundary values of fluxes and hydrodynamical parameters of the volume phases in the neighbourhood of the dividing surface. As an illustration of the general approach, the Maxwell boundary condition of gas slipping near hard surface is derived.